The radius of convergent of the power series #sum_ (n=1)^oo x^n/(n*2^n)# is?
The radius of convergent of the power series #sum_ (n=1)^oo x^n/(n*2^n)# is?
My answer is |x|<1.But I don't know whether that is correct.
The radius of convergent of the power series
My answer is |x|<1.But I don't know whether that is correct.
1 Answer
Explanation:
Here's the standard approach:
Using the ratio test, the series converges absolutolely when the below limit is strictly less than
where
Compute the limit:
Thus, the series converges for
Additional Notes
But what about when the test is inconclusive, or
Thus, the interval of convergence is